Find the current through the resistor ?1 given that ?=12.0V, ?1=4.73Ω, ?2=9.46Ω, ?3=23.65Ω, and ?4=14.19Ω.Group of answer choices 3.227 A1.289 A4.552 A4.973 A0.7882 A The image is a circuit diagram consisting of a voltage source $ V $ and four resistors $ R_1, R_2, R_3, $ and $ R_4 $.**Description:**1. **Voltage Source $ V $:** - Represents the electrical power supply for the circuit.2. **Resistor $ R_1 $:** - Connected in series with the voltage source.3. **Resistors $ R_2, R_3, $ and $ R_4 $:** - Connected in parallel with each other. - This parallel group is in series with $ R_1 $.**Circuit Layout:**- The current flows from the voltage source $ V $ through $ R_1 $.- After $ R_1 $, the current splits into three paths, going through $ R_2, R_3, $ and $ R_4 $ respectively, and then recombines into a single path completing the circuit.**Educational Focus:**- This diagram can be used to teach concepts such as series and parallel circuit configurations, Ohm's Law, and equivalent resistance calculations. Understanding how the total resistance changes based on configuration is crucial for analyzing and designing circuits.

Answered: Find the current through the resistor…

College Physics

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

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Find the current through the resistor ?1 given that ?=12.0V, ?1=4.73Ω, ?2=9.46Ω, ?3=23.65Ω, and ?4=14.19Ω.

Group of answer choices

3.227 A

1.289 A

4.552 A

4.973 A

0.7882 A

The image is a circuit diagram consisting of a voltage source $ V $ and four resistors $ R_1, R_2, R_3, $ and $ R_4 $.

**Description:**

1. **Voltage Source $ V $:**
- Represents the electrical power supply for the circuit.

2. **Resistor $ R_1 $:**
- Connected in series with the voltage source.

3. **Resistors $ R_2, R_3, $ and $ R_4 $:**
- Connected in parallel with each other.
- This parallel group is in series with $ R_1 $.

**Circuit Layout:**
- The current flows from the voltage source $ V $ through $ R_1 $.
- After $ R_1 $, the current splits into three paths, going through $ R_2, R_3, $ and $ R_4 $ respectively, and then recombines into a single path completing the circuit.

**Educational Focus:**
- This diagram can be used to teach concepts such as series and parallel circuit configurations, Ohm's Law, and equivalent resistance calculations. Understanding how the total resistance changes based on configuration is crucial for analyzing and designing circuits.

Expert Solution

Step 1

The equivalent resistance of the resistors $R_{2}, R_{3}, R_{4}$ connected in parallel is given by,

$\frac{1}{R_{eq,p}} = \frac{1}{R_{2}} + \frac{1}{R_{3}} + \frac{1}{R_{4}}$

Here, $R_{eq, p}$ is the equivalent resistance of the resistors $R_{2}, R_{3}, R_{4}$ connected in parallel.

Substituting,

$\begin{array}{rcl} \frac{1}{R_{eq,p}} & = & \frac{1}{9.46 Ω} + \frac{1}{23.65 Ω} + \frac{1}{14.19 Ω} \\ R_{eq,p} & = & 4.577 Ω \end{array}$

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